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  1. #1
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    Show that

    Show that
    cot^2(p/7) + cot^2(2p/7) + cot^2(3p/7) = 5.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by perash View Post
    Show that
    cot^2(p/7) + cot^2(2p/7) + cot^2(3p/7) = 5.
    For what value(s) of p? This is not true in general.

    -Dan

    EDIT: Aaaah. You meant p = \pi.
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  3. #3
    Senior Member JaneBennet's Avatar
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    See this: http://www.mathisfunforum.com/viewto...d=79371#p79371

    It was proved that \tan^2{\frac{\pi}{7}},\tan^2{\frac{2\pi}{7}},\tan^  2{\frac{3\pi}{7}} are the roots of the equation x^3-21x^2+35x-7=0.

    Hence \cot^2{\frac{\pi}{7}},\cot^2{\frac{2\pi}{7}},\cot^  2{\frac{3\pi}{7}} are the roots of the equation \left(\frac{1}{x}\right)^3-21\left(\frac{1}{x}\right)^2+35\left(\frac{1}{x}\r  ight)-7=0, i.e. of the equation 7x^3-35x^2+21x-1=0.
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